the largest class of algebraic hyper structures satisfying the module like axioms is the v h -module. in this paper, we consider the category of v h -modules and prove that the direct limit alwaysexists in this category. direct limits are defined by a universal property, and so are unique. the mostpowerful tool in order to obtain a module from a given v h - module is the quotient out procedure....

Pantograph-catenary is now the dominant form of current collection for modern electric trains because they can be used higher voltages. Faults in pantograph-catenary systems threaten operation and safety railway transportation. They need to continuously monitored controlled maintain safe transport. Pantograph may damaged as a result extreme weather conditions which affect its normal operation, ...